Question

How do you evaluate `4.24\times 4.24`?

Answer 1

`4.24 xx 4.24 = 17.9776`

Explanation:

Doing the calculation by hand, you could break it down as follows:

Starting with `4.24`, divide by `4` to get `1.06 = 1+0.06`

Then:

`4.24 xx 4.24 = 4 xx (1 + 0.06) xx 4 xx (1 + 0.06)`

`color(white)(4.24 xx 4.24) = 16 xx (1 + 0.06)^2`

`color(white)(4.24 xx 4.24) = 16 xx (1 + 2(0.06)+ 0.06^2)`

`color(white)(4.24 xx 4.24) = 16 xx (1 + 0.12 + 0.0036)`

`color(white)(4.24 xx 4.24) = 16 xx 1.1236`

`color(white)(4.24 xx 4.24) = 8 xx 2.2472`

`color(white)(4.24 xx 4.24) = 4 xx 4.4944`

`color(white)(4.24 xx 4.24) = 2 xx 8.9888`

`color(white)(4.24 xx 4.24) = 17.9776`

That may seem a little long-winded, but being able to double and halve numbers can often make arithmetic easier to do in your head.